Question

A sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 8.6 m/sm/s and at point B is 5.4 m/sm/s . Part A Use the impulse-momentum theorem to find how long the sled takes to travel from A to B.

Answer 1

Time taken by the sled is 1.31 s

Solution:

As per the question:

Coefficient of kinetic friction,
`\mu_(k) = 0.25`

Velocity at point A,
`v_(A) = 8.6\ m/s`

Velocity at point A,
`v_(B) = 5.4\ m/s`

Now,

To calculate the time taken by the sled to travel from A to B:

According to the impulse-momentum theorem, impulse and the change in the momentum of an object are equal:

Impulse, I = Change in momentum of the sled,
`\Delta p` (1)

`I = Ft` (2)

where,

F = Force

t = time

p = momentum of the sled

Force on the sled is given by:

`F = \mu_(k)N`

where

N = normal reaction force = mg

where

m = mass of the sled

g = acceleration due to gravity

Thus

`F = \mu_(k)mg` (3)

Using eqn (1), (2) and (3):

`\mu_(k)mgt = m\Delta v`

`\mu_(k)gt = v_(A) - v_(B)`

`t = (v_(A) - v_(B))/(\mu_(k)g)`

`t = (8.6 - 5.4)/(0.25* 9.8)`

t = 1.31 s

Answer 2

`\Delta t =1.31\ s`

Step-by-step explanation:

given,

coefficient of kinetic friction, μ = 0.25

Speed of sled at point A = 8.6 m/s

Speed of sled at point B = 5.4 m/s

time taken to travel from point A to B.

we know,

J = F Δ t

J is the impulse

where F is the frictional force.

t is the time.

we also know that impulse is equal to change in momentum.

`J = m(v_f - v_i)`

frictional force

F = μ N

where as N is the normal force

now,

`F\Delta t = m(v_f -v_i)`

`\mu m g * \Delta t = m(v_f-v_i)`

`\mu g * \Delta t = v_f-v_i`

`\Delta t =(v_f-v_i)/(\mu g)`

`\Delta t =(8.6-5.4)/(0.25* 9.8)`

`\Delta t =1.31\ s`

time taken to move from A to B is equal to 1.31 s